2005ApJ...630...59O

We investigate the prospects of future supernova searches getting meaningful constraints on the cosmic star formation history (CSFH) and the delay time of Type Ia supernovae from star formation (τ_Ia), based only on supernova data. Here we parameterized the CSFH by two parameters, α and β, which are the evolutionary indices [∝(1+z)^{{cubl0}α,β{cubr0}}] at z≳1 and ≲1, respectively, and quantitatively examined how well the three parameters (α, β, and τ_Ia) can be constrained in ongoing and future supernova surveys. We found that the type classification of detected supernovae down to the magnitude of I_AB∼27 is essential for getting a useful constraint on β. The parameter τ_Iacan also be constrained to within an accuracy of ∼1-2 Gyr without knowing α, which is somewhat degenerate with τ_Ia. This might be achieved by ground-based surveys but depends on the still highly uncertain type classification by imaging data. More reliable classification will be achieved by the SNAP mission. The supernova counts at a magnitude level of I_ABor K_AB∼30 will allow us to break degeneracies between α and τ_Iaand independently constrain all three parameters, even without knowing supernova types. This can be achieved by the SNAP and JWST missions, which have the different strengths of larger statistics and reaching to higher redshifts, respectively. The dependence of observable quantities on survey time intervals is also quantitatively calculated and discussed.